Finite Group Databasebeta

← C2×#27539 #6440965

Subgroups — C2×#27539 #6440965

Order 512.

3346 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2496C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3#27539C2116yesmaximal, direct product factor
4C2×#2077C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2071C211yesmaximal, characteristic, complemented
7C2×#2065C211yesmaximal, characteristic, complemented
8C2×#1936C211yesmaximal, characteristic, complemented
9C2×#1926C211yesmaximal, characteristic, complemented
10C2×#1924C211yesmaximal, characteristic, complemented
11C2×#1864C211yesmaximal, characteristic, complemented
12C2×#1864C211yesmaximal, characteristic, complemented
13C2×#1802C211yesmaximal, characteristic, complemented
14C2×#1786C211yesmaximal, characteristic
15C2×#1786C211yesmaximal, characteristic
16C2×#1762C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C22×#126—21no—
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C23×C22⋊C4—21no—
22C22×#106C2211yescharacteristic, complemented
23C22×#106C2211yescharacteristic, complemented
24C22×C4⋊C8C2211yescharacteristic, complemented
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×#97C2211yescharacteristic, complemented
36#2496—24no—
37#2496C2218yescomplemented
38C2×#400—21no—
39C2×#397—21no—
40D4×C22⋊C4—24no—
41D4×C22⋊C4C2218yes—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic, complemented
45C2×#389C2211yescharacteristic, complemented
46C2×#387—21no—
47C2×#386—21no—
48C2×#386—21no—
49C2×#384C2211yescharacteristic, complemented
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#379—21no—
54C2×C4×C4⋊C4C2211yescharacteristic, complemented
55C2×C4×C22⋊C4C2211yescharacteristic
56#2077C2218yescomplemented
57#2077C2218yescomplemented
58#2071C2218yescomplemented
59#2065C2218yescomplemented
60#1936C2218yescomplemented
61#1926C2218yescomplemented
62#1924C2218yescomplemented
63#1864C2218yescomplemented
64#1864C2218yescomplemented
65#1802C2218yescomplemented
66#1786C2218yes—
67#1786C2218yes—
68#1762C2218yescomplemented
69C2×#340C2211yescharacteristic, complemented
70C2×#340C2211yescharacteristic, complemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#336C2211yescharacteristic, complemented
76C2×#336C2211yescharacteristic, complemented
77C26—21no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—22no—
83C23×D4—21no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4C2311yescharacteristic
87C23×D4C2314yes—
88C23×D4C2311yescharacteristic
89C24×C4—21no—
90C24×C4—21no—
91C24×C4C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C2×#126—28no—
97C2×#126—48no—
98C2×C4×D4—24no—
99C2×C4×D4—24no—
100C2×C4×D4—22no—
101C2×C4×D4—22no—
102C2×C4×D4—42no—
103C2×C4×D4—42no—
104C2×C4×D4C2314yes—
105C2×C4×D4C2314yes—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—48no—
127C22×C22⋊C4D411yescharacteristic
128C22×C22⋊C4D411yescharacteristic
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C2×#106—42no—
133C2×#106—42no—
134C2×#106C2314yescomplemented
135C2×#106C2314yescomplemented
136C2×C4⋊C8—42no—
137C2×C4⋊C8C2314yescomplemented
138C2×#102—24no—
139C2×#102—24no—
140C2×#102—24no—
141C2×#102—24no—
142C2×#102—24no—
143C2×#102—24no—
144C2×#102—42no—
145C2×#102—42no—
146C2×#102C2314yes—
147C2×#102C2314yes—
148C2×#102C2314yes—
149C2×#102C2314yes—
150C2×#102C2314yes—
151C2×#102C2314yes—
152C2×#102C2314yes—
153C2×#102C2314yes—
154C2×C22⋊C8—42no—
155C2×C22⋊C8—42no—
156C2×C22⋊C8C2314yes—
157C2×C22⋊C8C2314yes—
158C2×#97—42no—
159C2×#97C2314yescomplemented
160#400—28no—
161#397—28no—
162#390—22no—
163#390—22no—
164#390C2314yes—
165#390C2314yes—
166#389—22no—
167#389—22no—
168#389C2314yescomplemented
169#389C2314yescomplemented
170#387—28no—
171#386—28no—
172#386—28no—
173#384—22no—
174#384C2314yescomplemented
175#380—22no—
176#380—22no—
177#380—22no—
178#380C2314yes—
179#380C2314yes—
180#380C2314yes—
181#379—28no—
182C4×C4⋊C4—22no—
183C4×C4⋊C4C2314yescomplemented
184C4×C22⋊C4D414yes—
185C4×C22⋊C4C2314yes—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95D411yescharacteristic
193C2×#95D411yescharacteristic
194#340C2314yescomplemented
195#340C2314yescomplemented
196#340C2314yescomplemented
197#340C2314yescomplemented
198#340C2314yescomplemented
199#340C2314yescomplemented
200#336C2314yescomplemented
201#336C2314yescomplemented
202C25—21no—
203C25—28no—
204C25—21no—
205C25—24no—
206C25—44no—
207C25—44no—
208C25—44no—
209C25—44no—
210C25—82no—
211C25—82no—
212C25C2×D411yescharacteristic
213C22×D4—28no—
214C22×D4—216no—
215C22×D4—28no—
216C22×D4—28no—
217C22×D4—28no—
218C22×D4—28no—
219C22×D4—21no—
220C22×D4—24no—
221C22×D4—21no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—48no—
233C22×D4—48no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—416no—
237C22×D4—416no—
238C22×D4—416no—
239C22×D4—416no—
240C22×D4#4114yes—
241C22×D4#4114yes—
242C22×D4#4114yes—
243C22×D4#4114yes—
244C22×D4C2412yes—
245C22×D4C2412yes—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—82no—
265C23×C4—82no—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8C2412yes—
287C22×C8C2412yes—
288C22×C8C2412yes—
289C22×C8C2412yes—
290#126—432no—
291C4×D4—28no—
292C4×D4—28no—
293C4×D4—44no—
294C4×D4—44no—
295C4×D4—48no—
296C4×D4—48no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2412yes—
324C2×C4⋊C4C2412yes—
325C2×C4⋊C4C2412yes—
326C2×C4⋊C4C2412yes—
327C2×C4⋊C4C2412yes—
328C2×C4⋊C4C2412yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—432no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—82no—
349C2×C22⋊C4—82no—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×D414yes—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—44no—
358C2×C42C2×D412yes—
359C2×C42C2×D412yes—
360C2×C42C2412yes—
361C2×C42C2412yes—
362#106—44no—
363#106—44no—
364C4⋊C8—44no—
365#102—28no—
366#102—28no—
367#102—28no—
368#102—28no—
369#102—28no—
370#102—28no—
371#102—44no—
372#102—44no—
373C22⋊C8—44no—
374C22⋊C8—44no—
375#97—44no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95C2×D414yes—
383#95C2×D414yes—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—216no—
395C24—24no—
396C24—22no—
397C24—48no—
398C24—48no—
399C24—48no—
400C24—432no—
401C24—432no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—48no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—84no—
414C24—84no—
415C24—816no—
416C24—816no—
417C24—816no—
418C24—816no—
419C24—816no—
420C24AGL(1,ℤ/8)14yes—
421C24C22×D412yes—
422C24C22×D411yescharacteristic
423C2×D4—216no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—48no—
442C2×D4—48no—
443C2×D4—416no—
444C2×D4—416no—
445C2×D4—416no—
446C2×D4—464no—
447C2×D4—432no—
448C2×D4—416no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4#126116yescomplemented
454C2×D4C2×#4114yes—
455C2×D4C2×#4114yes—
456C2×D4C2×#4114yes—
457C2×D4C2×#4114yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—48no—
513C22×C4—84no—
514C22×C4—84no—
515C22×C4—816no—
516C22×C4—816no—
517C22×C4AGL(1,ℤ/8)14yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D411yescharacteristic
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C4H(5,𝔽2)12yes—
530C22×C4C2511yescharacteristic
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—44no—
544C2×C8—44no—
545C2×C8—44no—
546C2×C8—44no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—48no—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—84no—
579C22⋊C4—84no—
580C42—24no—
581C42—24no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—48no—
587C23—28no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—216no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—432no—
602C23—432no—
603C23—48no—
604C23—44no—
605C23—48no—
606C23—44no—
607C23—48no—
608C23—48no—
609C23—48no—
610C23—44no—
611C23—42no—
612C23—42no—
613C23—48no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—48no—
618C23—48no—
619C23—42no—
620C23—42no—
621C23—48no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—816no—
627C23—816no—
628C23—816no—
629C23—8128no—
630C23—816no—
631C23—816no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23#52512yes—
637C23#54612yes—
638C23#54612yes—
639C23C2×AGL(1,ℤ/8)14yes—
640C23C2×AGL(1,ℤ/8)12yes—
641C23C2×AGL(1,ℤ/8)12yes—
642C23#57712yes—
643C23#57712yes—
644C23C23×D411yescharacteristic
645D4—24no—
646D4—24no—
647D4—24no—
648D4—24no—
649D4—24no—
650D4—216no—
651D4—432no—
652D4—42no—
653D4—42no—
654D4—48no—
655D4C2×#12618yescomplemented
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—816no—
699C2×C4—816no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4#52512yes—
707C2×C4C2×#12614yes—
708C2×C4#53814yes—
709C2×C4#54612yes—
710C2×C4#54612yes—
711C2×C4#55114yes—
712C2×C4#55114yes—
713C2×C4C2×AGL(1,ℤ/8)14yes—
714C2×C4C22×#4111yescharacteristic
715C2×C4C22×#4111yescharacteristic
716C2×C4C22×#4111yescharacteristic
717C2×C4C22×#4111yescharacteristic
718C2×C4C2×H(5,𝔽2)11yescharacteristic
719C2×C4C2×H(5,𝔽2)11yescharacteristic
720C8—42no—
721C8—42no—
722C8—42no—
723C8—42no—
724C22—28no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—44no—
730C22—42no—
731C22—44no—
732C22—416no—
733C22—432no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—42no—
738C22—44no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—864no—
744C22—816no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22#248014yes—
750C22#310914yes—
751C22#312314yes—
752C22#330614yes—
753C22#330614yes—
754C22#331014yes—
755C22#332414yes—
756C22C2×#52511yescharacteristic
757C22C2×#54611yescharacteristic
758C22C2×#54611yescharacteristic
759C22C22×AGL(1,ℤ/8)11yescharacteristic
760C22C22×AGL(1,ℤ/8)11yescharacteristic
761C22C2×#57711yescharacteristic
762C22C2×#57711yescharacteristic
763C4—24no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—82no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4#248014yes—
775C4C22×#12611yescharacteristic
776C4C2×#53811yescharacteristic
777C4C2×#55111yescharacteristic
778C4C2×#55111yescharacteristic
779C2—44no—
780C2—48no—
781C2—84no—
782C2#2753918yesdirect product factor
783C2C2×#248011yescharacteristic
784C2C2×#310911yescharacteristic
785C2C2×#312311yescharacteristic
786C2C2×#330611yescharacteristic
787C2C2×#330611yescharacteristic
788C2C2×#331011yescharacteristic
789C2C2×#332411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2496C2semidirect
3. #27539C2direct (N × H)
4. C2×#2077C2semidirect
5. C2×#2077C2semidirect
6. C2×#2071C2semidirect
7. C2×#2065C2semidirect
8. C2×#1936C2semidirect
9. C2×#1926C2semidirect
10. C2×#1924C2semidirect
11. C2×#1864C2semidirect
12. C2×#1864C2semidirect
13. C2×#1802C2semidirect
16. C2×#1762C2semidirect
22. C22×#106C22semidirect
23. C22×#106C22semidirect
24. C22×C4⋊C8C22semidirect
35. C22×#97C22semidirect
37. #2496C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
49. C2×#384C22semidirect
54. C2×C4×C4⋊C4C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2071C22semidirect
59. #2065C22semidirect
60. #1936C22semidirect
61. #1926C22semidirect
62. #1924C22semidirect
63. #1864C22semidirect
64. #1864C22semidirect
65. #1802C22semidirect
68. #1762C22semidirect
69. C2×#340C22semidirect
70. C2×#340C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#336C22semidirect
76. C2×#336C22semidirect
134. C2×#106C23semidirect
135. C2×#106C23semidirect
137. C2×C4⋊C8C23semidirect
159. C2×#97C23semidirect
168. #389C23semidirect
169. #389C23semidirect
174. #384C23semidirect
183. C4×C4⋊C4C23semidirect
194. #340C23semidirect
195. #340C23semidirect
196. #340C23semidirect
197. #340C23semidirect
198. #340C23semidirect
199. #340C23semidirect
200. #336C23semidirect
201. #336C23semidirect
453. C2×D4#126semidirect
655. D4C2×#126semidirect
782. C2#27539direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#24962
C2×D4×C22⋊C42
#275392
C2×#20772
C2×#20712
C2×#20652
C2×#19362
C2×#19262
C2×#19242
C2×#18642
C2×#18022
C2×#17862
C2×#17622